Two desirable attributes of lasers operable in the visible and infrared are high output power and tunable output wavelength. These attributes are available individually-existing carbon dioxide lasers are capable of providing 10 kilowatts or more output at a fixed wavelength, and there exist tunable lasers capable of providing variable visible wavelengths at output powers ranging from milliwatts up to approximately 10 watts. However, there have not heretofore been any lasers capable of providing both of the sought after attributes in a single device.
The free electron laser as described in U.S. Pat. No. 3,822,410 issued July 2, 1974 to John M. J. Madey has shown considerable promise in making available a tunable high power device. In a free electron laser, a relativistic electron beam is caused to interact with an electromagnetic wave in the presence of a transverse, periodic magnetic field. Assuming a TEM electromagnetic wave, the operating wave length .lambda. is given by: ##EQU1## where v.sub.par .ident.electron longitudinal velocity, measured parallel to the direction of propagation of the electromagnetic wave
c.ident.speed of light PA1 .lambda..sub.q .ident.magnet period, measured parallel to the direction of propagation of the electromagnetic wave. PA1 .alpha..sup.2 B.sup.2 .ident.(.lambda..sub.q eB/.sqroot.2.pi.mc.sup.2).sup.2 PA1 m.ident.electron rest mass (grams) PA1 e.ident.electron charge (statcoulombs) PA1 B.ident.rms amplitude of the periodic magnetic field PA1 .theta..ident.average angle at which electrons move through the interaction region, measured relative to the direction of propagation of the electromagnetic field. PA1 z.ident.longitudinal coordinate PA1 x.sub.0 (z).ident.nominal transverse position of electron with energy .gamma.mc.sup.2 PA1 x(z).ident.actual transverse position of electron.
This relationship follows from the requirement that the frequency of the electrons' spontaneous radiation match the frequency of the electromagnetic radiation to be amplified, or alternatively, that the electrons' transverse velocity remain synchronized with the optical electric field during the interaction. In systems involving wave propagation at velocities less than c, as in a wave guide or light pipe, c would be replaced by the phase velocity of the wave.
The electrons' longitudinal velocity is determined by their energy, the direction of their motion through the magnetic field, and the period and amplitude of the magnetic field. Thus, in a conventional free electron laser, the wavelength .lambda. is approximately given by: ##EQU2## where .gamma..sub.0 .ident.(electron energy)/mc.sup.2
While the dependence of wavelength on electron energy permits the free electron laser to be tuned by varying the electron beam energy, the dependence of wavelength on energy also introduces problems, especially where the electron energy is poorly defined. More particularly, if the electron energy spread is large, the phase match condition of Equation (1-1) will be violated for some portion of the electron distribution, and the laser gain and power output will be reduced.
One approach to solving this problem is the subject of copending U.S. patent application Ser. No. 55,163 of Smith et al., filed July 6, 1979, and entitled "Free Electron Laser." The technique disclosed therein is known as gain expansion and seeks to preserve the phase match condition for electrons of differing energies by causing the higher energy electrons to move through the periodic magnet in a region of higher magnetic field or at a larger angle .theta.. From Equations (1-1) and (1-2) it can be seen that the phase match condition (v.sub.par independent of energy) will be preserved so long as the electrons are dispersed in transverse position or angle such that the ratio (1+.alpha..sup.2 B.sup.2 +.gamma..sup.2 .theta..sup.2).sup.1/2 /.gamma. remains constant.
The deviation of the electrons' actual transverse coordinates from their nominal coordinates defines the "betatron amplitude" x.sub..beta. as follows: EQU x.sub..beta. (z)=x(z)-x.sub.0 (z) (1-3)
where
The magnitude of x.sub..beta. and its derivative x.sub..beta. ' with respect to z is a measure of the loss of correlation of the energy and transverse coordinates. The betatron amplitude will evolve, along with the energy, as the electron beam moves through the laser magnet. While the betatron motion is to some extent damped by the synchrotron radiation, the damping rate is typically small. If, in a gain-expanded storage ring free electron laser, the growth of x.sub..beta. and x.sub..beta. ' in a single passage through the laser exceeds the reduction of these quantities due to synchrotron damping, the betatron amplitude will grow from pass to pass through the laser, and the correlation of energy and transverse position will be lost.
Accordingly, there is presented the need for a free electron laser configuration wherein the growth of x.sub..beta. and x.sub..beta. ' is limited, so that degradation of the power output and efficiency of gain-expanded storage ring free electron lasers is avoided.